Nintendo doesn't include it in all their controllers either. Kind of a pain when you have to walk over to the console to turn it on if you're going to use the snes controller. Also frustrating that only some games will let you access the home menu with those, even if they otherwise work fine. (Especially the Nintendo provided emulators! Game boy works fine with a snes controller, but if you want to switch to something else, it's a hassle) F-Zero 99 supports it well though!
But there is no home button on Nintendo's first-party NES or SNES-style controllers, which I think are the ones more directly comparable to what we're talking about here.
(Not sure about the N64-style controllers; I've never actually seen one of those in the wild)
It looks like the N64 controller has a Home button [1], as does the Genesis [2] controller. Which makes it even more curiouser that the NES and SNES controllers don't. :(
Personally, I count the NES controllers as Joy-Cons, since they slot into the side of the system, as other Joy-Cons do. They don't fit in my Joy-Con charging dock or the Joy-Con grip that came with the system, though.
